“He captured it on the second day.” Lachish was a large and well-fortified city. That Joshua and his army could conquer it on the second day is a testimony of how many of the fighting men of Lachish had been killed in the earlier battles. The Assyrians had a very efficient and powerful army, and they had to take the time to build siege ramps to conquer Lachish.
“the mouth of the sword.” Used to show great destruction, as if the sword was eating its victims (see commentary on Josh. 6:21).
“all the souls.” That is, all the people. In the Hebrew text, the word “soul” is singular, “all the soul.” This could be understood as “all the life that was in it,” but the context and scope of the conquest are about people; the animals were booty, and so the translation “all the life” could be confusing in English. “All the soul” in this case means all the life that is in all the people.